Co-prime Numbers (also called Relatively Prime Numbers)

Two numbers are considered co-prime (or relatively prime) if their greatest common divisor (GCD) is 1. In other words, they have no common divisors other than 1.

For example:

• 8 and 15 are co-prime numbers because the GCD of 8 and 15 is 1.
• 12 and 15 are not co-prime numbers because their GCD is 3.

Key Points:

1. Co-prime numbers can be any pair of integers that don't share any common prime factors.
2. If one number is prime, it is co-prime with any other number that is not a multiple of that prime.
3. Co-prime numbers do not need to be prime themselves.

Examples of Co-prime Numbers:

• 5 and 9: GCD = 1, so they are co-prime.
• 14 and 15: GCD = 1, so they are co-prime.

Examples of Numbers that are NOT Co-prime:

• 6 and 9: GCD = 3, so they are not co-prime.
• 8 and 12: GCD = 4, so they are not co-prime.

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Would you like more details on how to calculate GCD or examples on this? Or do you have any other questions?

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Related Questions:

1. How do you calculate the GCD of two numbers?
2. What is the Euclidean algorithm for finding GCD?
3. How do co-prime numbers relate to the concept of LCM (Least Common Multiple)?
4. Can a pair of numbers with one being 1 be considered co-prime with any number?
5. Are prime numbers always co-prime with each other?

Tip: To quickly check if two numbers are co-prime, try factoring both numbers and see if they have any common prime factors. If they do, they aren't co-prime!